In labeling containers it is desirable to operate high speeds. In one type of labeling machine which has been successful, namely that of U.S. Pat. No. 4,500,386, if labeling is carried out at high speeds difficulties are encountered owing to the fact that the path of travel of the containers is S-shaped and undergoes an inflection at the junction of two circular paths having opposite curvature. At high speeds the change of direction at this point of inflection imposes strain on the machine and the containers. Also the machine of the '386 Patent employs a downstream guide or roll-on pad to hold the containers against the vacuum drum while the label is being wrapped. Containers of the same nominal size and shape frequently depart from the assumed or nominal size and shape, which may cause difficulties. Furthermore there is a need for precise registry of each container and the leading end of a label as the two come into tangent contact.